Abstract
In this paper, a new approximate analytical method is proposed for solving the fractional biological population model, the fractional derivative is described in the Caputo sense. This method is based upon the Aboodh transform method and the new iterative method, the Aboodh transform is a modification of the Laplace transform. Illustrative cases are considered and the comparison between exact solutions and numerical solutions are considered for different values of alpha. Furthermore, the surface plots are provided in order to understand the effect of the fractional order. The advantage of this method is that it is efficient, precise, and easy to implement with less computational effort.
Highlights
Fractional calculus is a field of Mathematics that consists of ordinary and partial derivatives of positive non-integer order, it has attracted huge attention because it provides practical models than the integer derivative [1,2,3,4,5,6], for comprehensive study on fractional calculus see [7,8,9,10,11].Integral transform for solving problems in science can be traced back to the work of P.S
A new iterative method was proposed by Daftardar–Gejji and Jafari [19] to solve functional equations, the solutions were presented in series form
Nonlinear SEI1 I2 R fractional-order epidemic model for the transmission of dynamics of HIV epidemics has been solved in [25] using generalized mean value theorem
Summary
Fractional calculus is a field of Mathematics that consists of ordinary and partial derivatives of positive non-integer order, it has attracted huge attention because it provides practical models than the integer derivative [1,2,3,4,5,6], for comprehensive study on fractional calculus see [7,8,9,10,11]. A new iterative method was proposed by Daftardar–Gejji and Jafari [19] to solve functional equations, the solutions were presented in series form. Several authors have used the new iterative method to solve linear and nonlinear fractional partial differential equations [20,21,22,23,24]. The main objective of this paper is to use Aboodh transform iterative method to obtain the approximate analytical solution of the time-fractional biological population model [30]. To reduce the computational effort and complexity, we proposed a new method called the Aboodh transform iterative method, which is a combination of the Aboodh transform and the new iterative method for solving the time-fractional biological population model which is the novelty of this study.
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